Fluid-solid Model Research Articles

Experimental Study on Fluid-Solid Coupling Seepage Flow in Putaohua Reservoir

According to existing fluid-solid coupling models, reasonable range and control technology of pressure depression cone has not be formed in Putaohua reservoir. In this paper, using laboratory experiment, the relationship between rock elastic-plastic deformation, single phase permeability of oil or water and relative permeability curves has been measured and the following important facts has been established: oil well bottom hole pressure which is lower than formation pressure is in a reasonable range during the initial stage of commissioning, and a gently pressure depression cone is formed between the formation and wellbore, that can reduce the permeability loss by compaction settlement and particle migration and return to production in reasonable bottom hole pressure while the water flooding takes effect and thus enhance the oil recovery.

Analysis on Stability of Powerhouse Slope under the Operation Water Level Condition of Tianhuaban Hydropower Station

Through numerical calculation on the stability of powerhouse slope by the coupling fluid-solid model of ABAQUS software, stability of powerhouse slope under the operation water level of Tianhuaban hydropower station has been evaluated. The results show that influence of pore pressure and the pore fluid effective velocity vector under the operation water level of Tianhuaban hydropower station has been limited on the scope of powerhouse slope from elevation 971m to 990m; the displacement concentration phenomenon has been existed on the scope of powerhouse slope from elevation 971m to 1010m, but the value of total displacement is smaller; influence on the stability of powerhouse slope under the operation water level is weaker; and on the scope of powerhouse slope from elevation 971m to 990m, the seepage phenomenon may be happened, and the waterproofing measures on this area must be strengthened. The achieved results can provide a research foundation for the stability of hydropower station slope on the periodic pore pressure disturbance.

Deterministic Method of Floor Rock Permeability Tensor of Mining over Confined Water and Application in Numerical Simulation

Based on equivalent continuum media theory of fractured rock mass, the author got the permeability tensor of floor strata in some mine according to core logging method, drilling imaging method and boring water injection method, and determined the floor rock permeability tensor using correction method. The author simulated the floor inrush problem by coupling fluid-solid theory and anisotropic flow model with FLAC3D software. The result shows that, the destroyed depth of floor and the confined water rising height are all slight when the coal mining workface is 150m apart from the fault, but they increase obviously when the coal mining workface is 30m apart from the fault, and are extremely easy to get through and casue water inrush through fault.

On the accuracy of CFD modeling of cyclic high heat flux divertor experiment

To investigate the heat removal capability of conceptual divertor cooling fingers, accurate computational fluid dynamics (CFD) analyses are indispensable. Although the cooling performance of the divertor finger has been successfully high-heat-flux tested under real DEMO conditions in a combined helium loop and electron beam facility at the Efremov Institute, Russia, an accompanying numerical simulation of the experiments is of great importance. This might help to better understand the complex thermo-hydraulic conditions with the aim of predicting other different load cases. To accurately reproduce the experimental boundary conditions, the Gaussian-like shape of the absorbed power was taken into account and the heat losses were estimated. Modeling of the structure thermal conductivity was also found to be an important source of modeling uncertainty. In the context of accurate modeling of experimental conditions, the effect of some modeling assumptions was evaluated. Transient simulations of the cyclic heat flux experiment were performed only for the solid part of the cooling finger to avoid excessively long computation times. The helium cooling was taken into account by the heat transfer coefficient (HTC) on the fluid–structure interface, obtained from the steady-state simulations of the full solid–fluid model. The HTC distribution did not vary with time throughout the entire transient simulation. The modeling error associated with such HTC approximation was estimated for the particular cyclic experiment. It is shown that the simulated temperature cycles on the top of experimental mock-up agree well with the measured data.

Mechanics of the foot Part 2: A coupled solid–fluid model to investigate blood transport in the pathologic foot

A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region.

A coupled fluid–solid model for problems in geomechanics: Application to sand production

AbstractSome of the most challenging problems in geomechanics involve the coupling between fluid flow and solid deformation. In this paper we briefly present an overview of existing coupling methods to problems involving fluid flow and deformation and describe testing of a new discrete‐based coupling method for problems in porous media. Modeled permeability and porosity distributions are compared to idealized packed assemblies and results are presented for simulations of steady flow through porous media. Previously published results for the coupled model focused on few or multiple particles in a fluid, whereas our results show good agreement to packed assemblies of particles (i.e. porous media). Finally, the two‐dimensional model is applied to sand production, a common problem in geomechanics. Sand production is defined as the co‐production of both a fluid and solid phase in oil and gas wells. In our models, we capture initial sand production associated with early‐time drawdown. Later‐time results show episodic sanding rates associated with formation stability and instabilities. Both observations are qualitatively consistent with laboratory and field observations. We find that high confining pressure inhibits the production of sand, through elevated interparticle contact forces. It is argued that these physically based models have a use in testing and evaluating competing hypotheses of sand production but their applicability is currently limited to small spatial and temporal scales. We believe these models bridge an important gap between the underlying physics of micro‐mechanical interactions of fluid and solid grains and the continuum descriptions of those systems. Copyright © 2010 John Wiley & Sons, Ltd.

Magnetically-actuated artificial cilia for microfluidic propulsion

In this paper we quantitatively analyse the performance of magnetically-driven artificial cilia for lab-on-a-chip applications. The artificial cilia are fabricated using thin polymer films with embedded magnetic nano-particles and their deformation is studied under different external magnetic fields and flows. A coupled magneto-mechanical solid-fluid model that accurately captures the interaction between the magnetic field, cilia and fluid is used to simulate the cilia motion. The elastic and magnetic properties of the cilia are obtained by fitting the results of the computational model to the experimental data. The performance of the artificial cilia with a non-uniform cross-section is characterised using the numerical model for two channel configurations that are of practical importance: an open-loop and a closed-loop channel. We predict that the flow and pressure head generated by the artificial cilia can be as high as 18 microlitres per minute and 3 mm of water, respectively. We also study the effect of metachronal waves on the flow generated and show that the fluid propelled increases drastically compared to synchronously beating cilia, and is unidirectional. This increase is significant even when the phase difference between adjacent cilia is small. The obtained results provide guidelines for the optimal design of magnetically-driven artificial cilia for microfluidic propulsion.

Numerical Formulation to Study Fluid-Solid Interfaces Excited by Elastic Waves

In this paper, the scattering of elastic waves in a fluid-solid interface is researched. The Indirect Boundary Element Method (IBEM) was used to study this wave propagation phenomenon in a 2D fluid-solid model. The source, represented by a Hankel´s function of the second kind, is always applied in the fluid. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. The approach presented is usually called IBEM as the sources’ strengths should be obtained as an intermediate step. This indirect formulation can give a deep physical insight to the analyst on the generated diffracted waves, because it is closer to the physical reality and can be regarded as a realization of Huygens’ Principle, which mathematically is fully equivalent to the classical Somigliana’s representation theorem. In order to gauge accuracy, the method was tested by comparing it to an analytical solution. A near interface pulse generates scattered waves that can be registered by sensors located in the fluid. Results are presented in time domain, where several aspects related to the different wave types that emerge from this kind of problems are pointed out.

Energy-conserving local time stepping based on high-order finite elements for seismic wave propagation across a fluid-solid interface

When studying seismic wave propagation in fluid-solid models based on a numerical technique in the time domain with an explicit time scheme it is often of interest to resort to time substepping because the stability condition in the solid part of the medium can be more stringent than in the fluid. In such a case, one should enforce the conservation of energy along the fluid-solid interface in the time matching algorithm in order to ensure the accuracy and the stability of the time scheme. This is often not done in the available literature and approximate techniques that do not enforce the conservation of energy are used instead. We introduce such an energy-conserving local time stepping method, in which we need to solve a linear system along the fluid-solid interface. We validate it based on numerical experiments performed using high-order finite elements. This scheme can be used in any other numerical method with a diagonal mass matrix.

Coupled Problems of Dynamics in Materially Incompressible Saturated Porous Media

AbstractThe mechanical behavior of saturated porous materials is largely governed by the interaction between the solid skeleton and the pore fluid. This interaction is particularly strong in dynamic problems and leads to numerical challenges especially in the case of incompressible constituents. In fact, the permeability plays a significant role in this coupling and influences the choice of a proper time integration scheme. Proceeding from the macroscopic Theory of Porous Media (TPM) within the isothermal and geometrical linear regime, the governing balance equations of the dynamic binary solid–fluid model are the solid and fluid momentum balances, and the overall volume balance of the biphasic mixture. This set of coupled partial differential equations (PDEs) is solved within the framework of the mixed Finite Element Method (FEM) applying two different time solution methods, viz., a monolithic implicit and a splitted implicit–explicit scheme. The time stepping algorithms are implemented into the FE program PANDAS and a Scilab FE routine and compared on a one–dimensional wave propagation example. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Multi-Phasic, Continuum Damage Mechanics Model of Mechanically Induced Increased Permeability in Tissues

AbstractRecently, we have reported enhanced permeability of tissues due to in vivo treatment with pulsed high intensity focused ultrasound (pHIFU). This new therapy has shown promise as a way of increasing the penetration of large drug molecules, both out of the vasculature and through the tissue. To date, no clear physical model of tissue exists that can account for these effects.A new model is proposed that clearly establishes the link between tissue structure and fluid flow properties on one hand, and the history of applied mechanical forces on the other. The model draws inspiration from two different theoretical fields of materials science, multi-phase theory and continuum damage mechanics. The theory differs from the traditional bi-phasic solid-fluid model of tissues in that the fluid part here is broken into trapped (moving with the solid) and free (moving through the solid) parts. A damage-like variable links the effective elasticity of the tissue to the ratio of the trapped to free fluids. As the damage increases, the tissue becomes, in effect, less stiff and more permeable. Release of elastic energy drives the process. A distribution of energy barriers opposes the process and governs how the fluid is released as damage increases.

Modelling of flow and wall behaviour in a mildly stenosed tube

In the present computational analysis, pulsatile flow and vessel wall behaviour in a simplified model of a stenosed vessel were investigated. Geometry of a 45% axisymmetrically stenosed (by area) cylindrical tube and a sinusoidal inflow waveform were simulated, with the fluid being assumed to be incompressible and Newtonian. The vessel wall was treated as a thick-walled, incompressible and isotropic material with uniform mechanical properties across the normal as well as the constricted segment. The study of fluid flow and wall motion was initially carried out separately using two commercial codes CFX4.2 and ABAQUS7 respectively. Their combined effects and interactions were later investigated through an iteratively coupled algorithm. Model validations on the rigid-wall fluid and static no-flow solid models were satisfactory, with Root Mean Square deviations of around 7% in centreline axial velocity between the prediction and measurement values for the rigid wall stenosis model, and 5% in circumferential stress for a cylindrical tube model under static loading when compared with the analytical solution. Results on velocity profiles, wall shear stress, intramural strain and stress for the rigid and compliant cases were all presented. Comparison between the rigid and compliant models revealed that, the flow separation layer distal to the stenosis was thicker and longer, and wall shear stress was slightly lower in the compliant model by less than 7.2%. Results obtained from the static wall model (with uniform pressure loading) and coupled fluid/wall interaction modelling of pulsatile flow showed qualitatively similar wall strain and stress patterns but considerable differences in magnitude. The radial and axial stresses were reduced by 31 and 8%, while the circumferential stress was increased by 13% due to the presence of pulsatile flow. Under the flow and structural conditions investigated, the effects of wall compliance were small, and did not change the flow and solid behaviours qualitatively in this case.

Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans

Fluid shear stress and mechanical wall stress may play a role in the formation of early atherosclerotic lesions, but these quantities are difficult to measure in vivo. Our objective was to quantify these parameters in normal subjects in a clinical setting, and to define regions of low wall shear stress and high mechanical stress. The right carotid bifurcations of five healthy male volunteers were investigated using a novel non-invasive technique which integrates magnetic resonance angiography, ultrasonography, tonometry and state-of-the-art computational fluid dynamics and solid mechanics models. Significant inter-subject variations in patterns as well as magnitude of wall shear stress and mechanical stress were found. In spite of individual variabilities, this study revealed that some regions of the artery wall are exposed simultaneously to low wall shear stress and high mechanical stress and that these regions correspond to areas where atherosclerotic plaque develops. The coexistence of regions of low wall shear stress and high tensile stress may be an important determinant of the formation of atheroma in human arteries.

THERMAL WAKE EFFECTS IN PRINTED CIRCUIT BOARDS

A simple, one-dimensional analytical model is presented that characterizes thermal wake effects for a convection cooled flat plate with discrete, surface mounted isoflux heat sources. Using integral solution techniques, the model predicts the temperature rise induced at downstream locations due to heating of the boundary layer by upstream sources. This analytical solution can be part of a coupled solid-fluid model to quickly and accurately evaluate conjugate heat transfer for air-cooled electronics applications. The thermal wake model is validated using numerical simulations for a wide range of test cases, and the average difference between the numerical results and analytical predictions is less than 2% for all test cases.

Numerical simulation of transient scattering from bodies and shells in a layered fluid–solid medium

Results from numerical simulation of transient scattering by 3-D objects immersed in seawater or buried in the bottom sediment are presented, and compared with data from a shallow-water experiment in the Baltic in which a bottom-penetrating parametric sonar was used for detection of submerged or buried objects. A range-independent fluid–solid model of the medium is used. The scatterers have smooth shape and are modeled as acoustically impenetrable or alternatively penetrable fluid-enclosed thin elastic shells. The dynamics of such shell-structured scatterers are described by Love’s equations for thin shells. A recently developed numerical technique, based on a frequency-domain boundary integral equation (BIE) formulation of the scattering problem, is used to compute the scattered field. The Green’s function of the layered medium is obtained by an adaptive transform integral method. The BIE is discretized by high-order B-splines, point collocation, and global numerical quadrature. The incident field may be excited by a point source, a point source array, or a plane wave. Scattering of transient fields is computed by Fourier synthesis of monofrequent field components. The composite simulation being highly parallelizable, a version for execution on workstation clusters under MPICH has been implemented, allowing for convenient handling of also computationally demanding broadband excitations.

The interfacial properties of a model of a nematic liquid crystal

We have used the theory developed in the previous paper to study the induced orientational order at simple models of a solid-liquid crystal (LC) interface. The LC is modelled by a Maier-Saupe type of anisotropic pairwise potential while the solid is modelled by an impenetrable wall which exerts an anisotropic external potential on the fluid molecules. Our theory treats both the solid-fluid and fluid-fluid potentials on a microscopic level which allows us to study the role played by these two types of interactions in the alignment of the fluid molecules at the solid surface. In particular, we study in detail the nature of the wetting of the solid-isotropic liquid interface by the nematic phase. We illustrate this by presenting the results of numerical calculations for the density and orientational order parameter profiles at the wetting transition for two different models of the solid substrate. We find that due to the weakness of the first order N/I bulk transition, the surface phase transition for z -3 substrate potentials is also weakly first order, in contrast with the results for isotropic systems. For exponential solid substrates the transition is found to depend on the range of the solid-fluid interaction; for short-ranged potentials the transition is continuous whereas for longer-ranged potentials the transition becomes more strongly first-order as the range of the interaction increases. This type of behaviour is in agreement with the results for isotropic solid-fluid interfaces. We calculate the pre-wetting lines for the two solid-fluid models. We find that the structure of the co-existing films as well as the surface critical point depend rather strongly on the model for the solid-fluid interaction. Finally, we compare the results of our theory with the results obtained from a phenomenological one-order parameter Landau-de Gennes theory and with some recent experimental results. We assess their validity and possible range of application.